Effective moduli for micropolar composite with interface effect

Circuits with composite moduli

This work studies the power of ACC circuits. These are circuits that have modular gates, in addition to the usual AND,OR,NOT. We are particularly interested in circuits where the modulus is a composite number. Our main result is that every ACC circuit of polynomial size and depth d can be reduced to a depth-2 circuit SYM◦AND of size 2(logn)O(d) . This improves exponentially the previously best-...

Bounds on the Effective Moduli of Composite Materials

Wilson quotients for composite moduli

An analogue for composite moduli m ≥ 2 of the Wilson quotient is studied. Various congruences are derived, and the question of when these quotients are divisible by m is investigated; such an m will be called a “Wilson number”. It is shown that numbers in certain infinite classes cannot be Wilson numbers. Eight new Wilson numbers up to 500 million were found.

Effective moduli for thermopiezoelectric materials with microcracks

Dilute, Self-Consistent (SC), Mori–Tanaka (MT) and differential micromechanics methods are developed for microcrack-weakened thermopiezoelectric solids. These methods are capable of determination of effective properties such as the conductivity, electroelastic moduli, thermal expansion and pyroelectric coefficients. The above material constants affected by the microcracks are derived by way of ...

Exact relations for effective moduli of polycrystals

Composite materials play an increasingly important role in our everyday life and technology from skis and golf clubs to sensors and actuators in high tech components. By “composite” we mean a perfectly bonded homogeneous mixture of two or more materials on a length scale much smaller than human size and much larger than interatomic distances. The physical properties of a composite (conducting, ...